Electrode Arrangements for Quadrature Suppression in Inertial Sensors

ABSTRACT

A substrate for an inertial sensor system includes a plurality of electrode arrangements, each electrode arrangement including an acceleration sensor electrode and a pair of quadrature adjusting electrodes on opposite sides of the acceleration sensor electrode, where each electrode arrangement is capable of being overlaid by a corresponding plate of a shuttle such that the plate completely overlays the acceleration sensor electrode and partially overlays the pair of quadrature adjusting electrodes on opposite sides of the acceleration sensor electrode such that capacitive coupling between the plate and each of the quadrature adjusting electrodes is dependent upon the rotational position of the at least one shuttle while capacitive coupling between the plate and the acceleration sensor electrodes is substantially independent of the rotational position of the at least one shuttle.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This patent application is a divisional of, and therefore claimspriority from, U.S. patent application Ser. No. 13/442,010 filed Apr. 9,2012 (Attorney Docket No. 2550/D83), which is a divisional of, andtherefore claims priority from, U.S. patent application Ser. No.12/469,899 filed May 21, 2009 (U.S. Pat. No. 8,151,641; Attorney DocketNo. 2550/C21); each of these patent applications is hereby incorporatedherein by reference in its entirety.

TECHNICAL FIELD

The present invention relates to micromachined inertial sensors, andmore particularly to mode matching in micromachined inertial sensors.

BACKGROUND ART

Micromachined (MEMS) gyroscopes have become established as usefulcommercial items. Generally speaking, a MEMS gyroscope incorporates twohigh-performing MEMS devices, specifically a self-tuned resonator in thedrive axis and a micro-acceleration sensor in the sensing axis.Gyroscope performance is very sensitive to such things as manufacturingvariations, errors in packaging, driving, linear acceleration, andtemperature, among other things. Basic principles of operation ofangular-rate sensing gyroscopes are well understood and described in theprior art (e.g., Geen, J. et al., New iMEMS Angular-Rate-SensingGyroscope, Analog Devices, Inc., Analog Dialog 37-03 (2003), availableathttp://www.analog.com/library/analogDialogue/archives/37-03/gyro.html,which is hereby incorporated herein by reference in its entirety).

The principles of vibratory sensing angular rate gyroscopes withdiscrete masses are long-established (see, for example, Lyman, U.S. Pat.No. 2,309,853 and Lyman, U.S. Pat. No. 2,513,340, each of which ishereby incorporated herein by reference in its entirety). Generallyspeaking, a vibratory rate gyroscope works by oscillating a proof mass(also referred to herein as a “shuttle” or “resonator”). The oscillationis generated with a periodic force applied to a spring-mass-dampersystem at the resonant frequency. Operating at resonance allows theoscillation amplitude to be large relative to the force applied. Whenthe gyroscope is rotated, Coriolis acceleration is generated on theoscillating proof mass in a direction orthogonal to both the drivenoscillation and the rotation. The magnitude of Coriolis acceleration isproportional to both the velocity of the oscillating proof mass and therotation rate. The resulting Coriolis acceleration can be measured bysensing the deflections of the proof mass. The electrical and mechanicalstructures used to sense such deflections of the proof mass are referredto generally as the accelerometer.

Many MEMS gyroscopes employ balanced comb drives of the type describedgenerally in Tang, U.S. Pat. No. 5,025,346, which is hereby incorporatedherein by reference in its entirety. General use of a micromachinedlayer above a semiconductor substrate with Coriolis sensingperpendicular to that substrate is described generally in Zabler, U.S.Pat. No. 5,275,047, which is hereby incorporated herein by reference inits entirety. Exemplary MEMS gyroscopes are described in Bernstein, U.S.Pat. No. 5,349,855; Dunn, U.S. Pat. No. 5,359,893; Geen, U.S. Pat. No.5,635,640; Geen, U.S. Pat. No. 5,869,760; Zerbini, U.S. Pat. No.6,370,954; and Geen U.S. Pat. No. 6,837,107, each of which is herebyincorporated herein by reference in its entirety. The latter fourpatents employ rotationally vibrated mass(es).

One problem in the manufacture of MEMS gyroscopes is that the Coriolissignals on which they depend are relatively small. It has been longrecognized (e.g. Ljung, U.S. Pat. No. 4,884,446 or O'Brien, U.S. Pat.No. 5,392,650 or Clark, U.S. Pat. No. 5,992,233, each of which is herebyincorporated herein by reference in its entirety) that the signal sizeof a vibratory gyroscope can be magnified by operating the Coriolisaccelerometer at resonance, i.e., by matching the frequencies of theaccelerometer to that of the vibrating shuttle. Generally speaking, thisincrease in signal size eases the associated electronics requirementsand thereby reduces cost. However, generally speaking, the larger theresonant amplification, the more sensitive is the accelerometer phaseshift to small frequency perturbations. Such phase shifts areparticularly deleterious to gyroscope performance, so it is generallynecessary, in practice, to either well separate the frequencies ortightly servo the frequency of the accelerometer to the frequency of theshuttle. A mechanism for controlling the frequency of a differentialcapacitance accelerometer is conveniently available from changing theapplied common mode voltage.

One technique for sensing the frequency match in order to close a servoloop around that mechanism is to apply a small, periodic perturbation tothe mechanism and servo to zero response modulated at that periodicity.This is analogous to the mode matching servo commonly used in lasergyroscopes (e.g. Ljung, U.S. Pat. No. 4,267,478 or Curley, U.S. Pat. No.4,755,057, each of which is hereby incorporated herein by reference inits entirety). This method uses the quadrature signal which directlycouples from the shuttle and which can be separated from the useful,in-phase signal by synchronous demodulation. In practice, the magnitudeof that signal generally varies widely and therefore is generally alsosubject to some control mechanism if the mode-matching servo is to havedefined gain. This would be straightforward were it not that a realsystem generally has some other phase errors so that, for best gyroperformance, the magnitude of quadrature signal should be near zero.

Another, method would be to apply a shuttle-frequency signalelectromechanically to the accelerometer and synchronously demodulatethe displacement output, servoing for the null which occurs at the 90degree resonant phase shift. This inevitably interferes with theCoriolis signal and effectively is only applicable to those gyroscopesthat do not need static response, such as camera stabilizing gyros.

The problem is addressed, at the expense of complexity, in Thomae, U.S.Pat. No. 6,654,424, which is hereby incorporated herein by reference inits entirety, by applying two such signals symmetrically disposed aboutthe desired resonance and servoing for equality of response from them.This involves two signal generators, two demodulators, two filters and adifferencing means, over twice the circuitry which one might otherwiseexpect for the servo.

In vibratory rate gyroscopes, numerous factors, such as imperfections inthe various mechanical structures and in the electronics used fordriving and sensing, can cause oscillations of the accelerometer thatcan be confused with Coriolis acceleration and rotation rate. Such errorsources are often referred to collectively as gyroscope offset. Thereare two main classes of gyroscope offset, namely in-phase error andquadrature error. Generally speaking, quadrature error results when thevibratory motion is not perfectly orthogonal to the accelerometer. Inthe presence of quadrature error, the accelerometer experiencesdeflections proportional to the driven displacement. In-phase errorresults when the vibratory drive force is not perfectly orthogonal tothe accelerometer. With in-phase error, the accelerometer experiencesdeflections proportional to the oscillation driving force which, atresonance, is also proportional to the oscillation velocity. Gyroscopeoffset can vary over time, for example, due to changes in temperature.

One possible approach to reducing gyroscope offset is to attempt tominimize the offset through device design, manufacture, and packaging,but there are practical limits to this approach.

SUMMARY OF THE INVENTION

In a first embodiment there is provided n inertial sensor comprising (1)a substrate having a plurality of electrode arrangements, each electrodearrangement including an acceleration sensor electrode and a pair ofquadrature adjusting electrodes on opposite sides of the accelerationsensor electrode; and (2) a resonator disposed in a device layer abovethe substrate and having at least one shuttle including a plurality ofplates, each plate completely overlaying a corresponding accelerationsensor electrode and partially overlaying the pair of quadratureadjusting electrodes on opposite sides of the acceleration sensorelectrode, such that capacitive coupling between the plate and each ofthe quadrature adjusting electrodes is dependent upon the rotationalposition of the at least one shuttle while capacitive coupling betweenthe plate and the acceleration sensor electrodes is substantiallyindependent of the rotational position of the at least one shuttle.

In various alternative embodiments, the inertial sensor may include aplurality of drive electrodes disposed in the device layer forrotationally dithering the at least one shuttle in a device layer plane.The inertial sensor may include a shuttle resonance drive servo coupledto the drive electrodes, the shuttle resonance drive servo configured toprovide drive signals to the drive electrodes for rotationally ditheringthe at least one shuttle in the device layer plane. The inertial sensormay include a quadrature servo coupled to the quadrature adjustingelectrodes, the quadrature servo configured to provide quadraturenullifying signals to the quadrature adjusting electrodes. Thequadrature nullifying signals may be DC quadrature adjustment signals.

In further alternative embodiment, each shuttle may include an outer rimsuspended via a number of spokes from a central hub. The substrate mayinclude, for each of a number of spokes, a pair of quadrature adjustingelectrodes on the substrate underlying the radial edges of the spoke.The inertial sensor may include a quadrature servo coupled to thequadrature adjusting electrodes of the electrode arrangements andcoupled to the quadrature adjusting electrodes underlying the radialedges of the spokes, the quadrature servo configured to providequadrature nullifying signals to the quadrature adjusting electrodes.The quadrature nullifying signals may be DC quadrature adjustmentsignals.

In further alternative embodiments, the inertial sensor may include atest signal generator coupled to the quadrature adjusting electrodes,the test signal generator configured to provide a test signal to thequadrature adjusting electrodes at a test signal frequency above apredetermined quadrature servo response frequency. The inertial sensormay include a mode matching servo coupled to the test signal generatorand to the acceleration sensor electrodes, the mode matching servoconfigured to demodulate acceleration sensor signals received from theacceleration sensor electrodes with the test signal received from thetest signal generator and to produce therefrom a bias signal. The modematching servo may be coupled to the at least one shuttle to place thebias signal on the at least one shuttle or may be coupled to anelectrode on the substrate underlying the at least one shuttle to placethe bias signal on the said electrode.

In any of the above-embodiments, each electrode arrangement may includea phase-compensating electrode.

The resonator may include two shuttles that are mechanically coupled bya coupling flexure to ensure that the shuttles oscillate in anti-phasewith one another.

In a second embodiment there is provided an apparatus for use with aresonator having at least one shuttle including a plurality of plates,the apparatus comprising a substrate having a plurality of electrodearrangements, each electrode arrangement including an accelerationsensor electrode and a pair of quadrature adjusting electrodes onopposite sides of the acceleration sensor electrode, each electrodearrangement capable of being overlaid by a corresponding plate of the atleast one shuttle such that the plate completely overlays theacceleration sensor electrode and partially overlays the pair ofquadrature adjusting electrodes on opposite sides of the accelerationsensor electrode such that capacitive coupling between the plate andeach of the quadrature adjusting electrodes is dependent upon therotational position of the at least one shuttle while capacitivecoupling between the plate and the acceleration sensor electrodes issubstantially independent of the rotational position of the at least oneshuttle.

In various alternative embodiments, the substrate may further include atleast one electrical connection for providing quadrature nullifyingsignals to the quadrature adjusting electrodes.

In further alternative embodiments, the substrate may further include atleast one pair of quadrature adjusting electrodes configured to beoverlaid by the radial edges of a corresponding spoke of the at leastone shuttle. The substrate may include at least one electricalconnection for providing quadrature nullifying signals to the quadratureadjusting electrodes of the electrode arrangements and to the quadratureadjusting electrodes underlying the radial edges of the spokes.

In any of the above-embodiments, each electrode arrangement may includea phase-compensating electrode.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of the invention will be more readily understoodby reference to the following detailed description, taken with referenceto the accompanying drawings, in which:

FIG. 1 is a schematic top-view diagram of a vibratory X-Y axis gyroscopein accordance with an exemplary embodiment of the present invention,highlighting the device layer structures;

FIG. 2 is a schematic top-view diagram of a vibratory X-Y axis gyroscopein accordance with an exemplary embodiment of the present invention,highlighting the substrate layer structures in relation to the devicelayer structures highlighted in FIG. 1;

FIG. 3 is a schematic block diagram showing electronic circuitrysuitable for use with the gyroscope of FIGS. 1 and 2, in accordance withan exemplary embodiment of the present invention;

FIGS. 4-6 are schematic diagrams of idealized waveforms for thedescription of the electronic circuitry shown in FIG. 3;

FIG. 7A and FIG. 7B is a schematic top-view diagram of a vibratorygyroscope in accordance with an alternative embodiment of the presentinvention, in which FIG. 7A is a top view of the structures and FIG. 7Bis a magnified view of certain structures;

FIG. 8 is a schematic top-view diagram of an exemplary vibratory Z axisgyroscope in accordance with another alternative embodiment of thepresent invention;

FIG. 9 shows a detailed view of quadrature adjusting electrodes of thegyroscope shown in FIG. 8;

FIG. 10 is a schematic top-view diagram of a cross-quad Z axis gyroscopein accordance with another alternative embodiment of the presentinvention;

FIG. 11 shows a specific cross-quad gyroscope configuration that can beadapted for mode matching, in accordance with the embodiment shown inFIG. 10; and

FIG. 12 shows an exemplary variable-overlap electrode configuration inaccordance with the embodiment shown in FIG. 11.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

Definitions. As used in this description and the accompanying claims,the following terms shall have the meanings indicated, unless thecontext otherwise requires.

A “set” includes one or more elements.

An “electrode” is a structure through which an electrical orelectromechanical effect is applied and/or sensed. In exemplaryembodiments, various electrodes are used for applying and/or sensingelectrical or electromechanical effects through capacitive coupling,although it should be noted that other types of electrodes and couplingsmay be used (e.g., piezoelectric).

The term “quality factor” or “Q-factor” or simply “Q” denotes adimensionless parameter that compares the time constant for decay of anoscillating physical system's amplitude to its oscillation period.Equivalently, it compares the frequency at which a system oscillates tothe rate at which it dissipates its energy. A higher Q indicates a lowerrate of energy dissipation relative to the oscillation frequency, so theoscillations die out more slowly. A system with a high Q resonates witha greater amplitude (at the resonant frequency) than one with a low Qfactor, and its response falls off more rapidly as the frequency movesaway from resonance. The term “Q” may also be used as a shorthand torefer to the resonance frequency of the resonator.

The “mode” of a resonating body is the shape of motion of the body atresonance.

The “response frequency” of an inertial sensor is the maximum angularacceleration rate that can be sensed. The response frequency may berepresented by the pass frequency of a low-pass filter used to producethe inertial sensor output signal.

Exemplary embodiments of the present invention provide a relativelysimple, mode frequency matching servo that does not disturb the Coriolissignal and uses an easily generated single-frequency test signal. Themotion of a resonating gyroscope shuttle is amplitude modulated by thetest signal so as to electromechanically induce signals in the Coriolischannel. The induced signals in the Coriolis channel are essentially asum and difference of the shuttle mode frequency and the test signalfrequency. Thus, the Coriolis channel signals include the Coriolissignals induced by external rotation of the gyroscope (i.e., the angularacceleration being sensed) as well as electromechanically modulatedsignals induced by modulating the motion of the shuttles. These signalsare demodulated with the mathematical product of the test signal withshuttle frequency signal in order to produce a feedback bias signal thatis applied to appropriate gyroscope structures. In exemplaryembodiments, the test signal is applied to variable-overlap electrodes(e.g., electrodes used for quadrature adjustments) underlying an X-Yaxis gyroscope or in the device plane of a Z axis gyroscope, and thebias signal is applied to the sensing electrodes or other completelyoverlapping electrodes underlying an X-Y axis gyroscope or in the deviceplane of a Z axis gyroscope. The test signal amplitude modulates thequadrature motion of the gyroscope and the feedback bias effectivelysoftens the sensing Coriolis accelerometer springs electrically tomodify the accelerometer resonance frequency (i.e., the bias acts as anegative spring). Coincidence of that frequency with the shuttlefrequency is characterized by a 90 degree phase shift in theaccelerometer response and is sensed by the phase sensitivecharacteristic of demodulation.

FIGS. 1 and 2 are schematic top-view diagrams of a vibratory X-Y axisgyroscope 100 in accordance with an exemplary embodiment of the presentinvention. This vibratory gyroscope operates generally as disclosed inGeen, U.S. Pat. No. 5,635,640, which is hereby incorporated herein byreference in its entirety. Specifically, this vibratory gyroscopeincludes various micromachined gyroscope structures in a device layeroriented above an underlying substrate having various substrate layerstructures. For convenience, relevant gyroscope structures are describedbelow with reference to axes labeled “a” and “b” in the device plane.The axes labeled “x” and “y” represent the axes about which Coriolisacceleration is sensed (i.e., the gyroscope sensing axes).

The gyroscope structures in the device plane include tworotationally-dithered masses (referred to hereinafter as shuttles) 102and 104, each including an outer rim suspended via a number of spokes(in this case, twelve spokes, although different embodiments may usedifferent numbers of spokes) from a central hub that is movably coupledto the substrate via a post (shaped like a “+”) and suspension flexures101 (for convenience, only one of the two post and suspension flexurearrangements is highlighted). The posts are affixed to the substrate,and the suspension flexures allow the shuttles to oscillaterotationally, with coupling flexure 106 and support flexures 108 and 110helping to ensure that the shuttles oscillate in anti-phase with oneanother (i.e., shuttle 104 rotates counterclockwise when shuttle 102 isrotating clockwise, and vice versa) nominally within the device plane.For convenience, the dithered gyroscope structures in the device planemay be referred to collectively as a resonator.

Each of the spokes includes finger structures that interdigitate withcorresponding comb structures affixed to the substrate (for convenience,only two of the twenty-four sets of combs are highlighted, with each setincluding two combs). In this exemplary embodiment, the twenty-four setsof combs are used for driving motion of the shuttles, where one comb ineach pair is used for driving the shuttle in a clockwise direction andthe other is used for driving the shuttle in a counterclockwisedirection, specifically by applying alternating electrical signals tothe combs to cause the shuttles 102 and 104 to oscillate throughcapacitive coupling with the finger structures of the spokes. Velocitysensing electrodes are used in a feedback loop to sense and controloscillation of the shuttles. In this exemplary embodiment, velocitysensing electrodes 130 on the substrate underlying the radial edges ofthe a-oriented and b-oriented spokes (i.e., four spokes of each shuttle)are used for velocity sensing (for convenience, only one of the eightpairs of velocity sensing electrodes is highlighted).

In this exemplary embodiment, each of the shuttles includes fourprotruding plates that overlie corresponding electrode arrangements onthe substrate, with each electrode arrangement including aCoriolis-sensing electrode, a phase-compensating electrode, and a pairof quadrature electrodes on either side of the Coriolis-sensing andphase-compensating electrodes. Specifically, shuttle 102 includes plates112, 114, 116, and 118 that respectively overlie arrangements (112C,112P, 112Q), (114C, 114P, 114Q), (116C, 116P, 116Q), and (118C, 118P,118Q), while shuttle 104 includes plates 120, 122, 124, and 126 thatrespectively overlie arrangements (120C, 120P, 120Q), (122C, 122P,122Q), (124C, 124P, 124Q), and (126C, 126P, 126Q), where “C” designatesthe Coriolis-sensing electrode, “P” designates the phase-compensatingelectrode, and “Q” designates the quadrature electrodes. Each platecompletely overlies the Coriolis-sensing and phase-compensatingelectrodes but only partially overlies the quadrature electrodes, suchthat capacitive coupling between the plate and each of the quadratureelectrodes is dependent on the rotational position of the shuttle whilecapacitive coupling between the plate and the Coriolis-sensing andphase-compensating electrodes is substantially independent of therotational position of the shuttle. In this exemplary embodiment, theplates are positioned so as to align with the x and y axes (i.e., atapproximately 45 degree angles relative to the a and b axes). It shouldbe noted that, in this exemplary embodiment, the Coriolis-sensingelectrodes are not aligned with any of the drive combs 128. The variouselectrodes are discussed in more detail below.

While the shuttles are oscillating at their resonance frequency (fo),driven via the drive combs 128 with feedback provided via the velocitysensing electrodes 130, out-of-plane movements of the gyroscope aboutthe x and y axes cause the shuttles 102 and 104 to tip out-of-planerelative to the substrate through Coriolis forces, and theseout-of-plane (i.e., Coriolis axis) movements of the shuttles aredetected via the Coriolis-sensing electrodes through capacitive couplingwith the plates. In this exemplary embodiment, such Coriolis forces aresensed in two axes by differential capacitance with respect to theCoriolis-sensing electrodes. For example, a rotation of the gyroscopeabout the x-axis can cause plates 114 and 124 to move toward theirrespective Coriolis-sensing electrodes while plates 118 and 120 moveaway from their respective Coriolis-sensing electrodes, and thesemovements are detected by changes in capacitance between each plate andits corresponding Coriolis-sensing electrode, with the signals obtainedfrom the four Coriolis-sensing electrodes combined to provide agyroscope output signal representing the movement of the gyroscope.Similarly, a rotation of the gyroscope about the y-axis can cause plates116 and 126 to move toward their respective Coriolis-sensing electrodeswhile plates 112 and 122 move away from their respectiveCoriolis-sensing electrodes. It should be noted that the plates 112,114, 116, 118, 120, 122, 124, and 126 fully overlay their respectiveCoriolis-sensing electrodes throughout the entire rotational range ofmotion of the shuttles so that signals obtained from theCoriolis-sensing electrodes are substantially independent of therotational displacement of the shuttles.

Thus, the gyroscope resonator can be characterized by two modes, namelya shuttle resonance mode (i.e., the mode of the shuttles in the deviceplane) and an accelerometer resonance mode (i.e., the mode of theshuttles in the Coriolis axis). It is generally desirable for the twomodes to match, as this tends to increase signal-to-noise ratio of thegyroscope. In embodiments of the present invention, the accelerometerresonance mode frequency is generally higher than the shuttle resonancemode frequency and the two modes are matched by effectively decreasingthe accelerometer resonance mode frequency until it matches the shuttleresonance mode frequency, as discussed below.

Furthermore, even in the absence of any external movement of thegyroscope, oscillation of the shuttles typically results in slightout-of-plane movements of the shuttles, for example, due to imbalancesin the shuttles and their respective support structures, and suchout-of-plane movements of the shuttles can be misinterpreted as Coriolissignals and therefore represent error signals. As discussed above, sucherror signals may include an in-phase component and a quadraturecomponent. While the quadrature error signals can be substantiallygreater than the phase error signals and therefore can swamp electroniccircuitry that compensates for phase errors, it is generally desirableto remove both error components. In a gyroscope of the type shown inFIGS. 1 and 2, where the accelerometer resonance mode is out-of-planewith the shuttle resonance mode, it is generally impractical to usemechanical structures (e.g., levers and flexures) to eliminate thequadrature and in-phase error components.

Therefore, in a manner similar to that described by Clark in U.S. Pat.No. 5,992,233 or Geen in U.S. Pat. No. 7,032,451, each of which ishereby incorporated herein by reference in its entirety, quadratureadjustments are made by exerting a net torque on the shuttles in theCoriolis axis (i.e., out of the device plane). Quadrature suppression isalso discussed in Lemkin, U.S. Pat. No. 7,051,590; in Chaumet, U.S.Patent Application Publication No. 2008/0282833; and in Saukoski, M.,System and Circuit Design for a Capacitive MEMS Gyroscope, DoctoralDissertation, TKK Dissertations 116, Helsinki University of Technology,Espoo, Finland (2008), each of which is hereby incorporated herein byreference in its entirety.

In the exemplary embodiment shown in FIGS. 1 and 2, quadrature adjustingelectrodes on the substrate positioned under the edges of the plates(i.e., quadrature adjusting electrodes 112Q, 114Q, 116Q, 118Q, 120Q,122Q, 124Q, and 126Q) as well as under the radial edges of the eightspokes of each shuttle positioned between the a-oriented and b-orientedspokes (i.e., quadrature adjusting electrodes 132; for convenience, onlyfour of the sixteen pairs of quadrature adjusting electrodes 132 arehighlighted) are used for making quadrature adjustments, although inalternative embodiments, similar quadrature adjustments can be made byapplying bias voltages to the Coriolis sensing electrodes. A DCquadrature adjustment signal is applied to the quadrature adjustingelectrodes so as to exert a net torque on the shuttles. Since thequadrature adjusting electrodes extend beyond the edges of the platesand spokes, the torque produced by the quadrature adjusting electrodesis proportional to the vibratory displacement of the shuttles in thedevice plane and is a function of the difference between the potentialsof the electrodes. Thus, the torque causes a quadrature motion in theCoriolis axis (i.e., the axis normal to the device plane) that ismodulated by the potential of the quadrature adjusting electrodes.

It should be noted that some of the combs may be used for velocitysensing in addition to, or in lieu of, separate velocity sensingelectrodes. It also should be noted that the velocity sensing electrodes130 and the quadrature adjusting electrodes are somewhatinterchangeable; a particular pair of electrodes may be used forvelocity sensing and/or quadrature adjustment as desired for aparticular implementation.

In practice, in can be difficult to match the accelerometer resonancemode with the shuttle resonance mode, in part because the rotationalfrequency of the shuttles generally changes over time, for example, dueto temperature changes and other factors. Therefore, in embodiments ofthe present invention, a high-frequency test (carrier) signal is appliedto the quadrature adjusting electrodes to induce accelerometer signalsin the Coriolis channel that are 90 degrees phase shifted with respectto the Coriolis acceleration signal (i.e., the quadrature adjustingelectrodes generate a quadrature output modulated by the input testsignal), and the accelerometer resonance mode is adjusted by placing anappropriate biasing voltage on the gyroscope structures until there areno Coriolis channel signals at the test signal frequency. Thus, the testsignal applied to the quadrature adjusting electrodes causes thequadrature motion of the shuttles to be amplitude modulated with thetest frequency in the Coriolis axis. The test signal is provided at afrequency sufficiently above the gyroscope response frequency, so thatthe test signal is not detected by the signal filtering in the Coriolischannel and therefore does not affect the gyroscope output, but at afrequency sufficiently below the accelerometer resonance mode frequency,so that the Coriolis accelerometer will respond to the test signals. Forexample, in an exemplary embodiment, the gyroscope response frequencymay be below approximately 32 Hz, and the shuttle resonance modefrequency (fo) may be approximately 64 KHz, and the test signalfrequency may be an integer fraction of the shuttle resonance modefrequency, e.g., between approximately 1 KHz to 8 KHz (i.e., fo/64 tofo/8). Furthermore, the test signal preferably averages to zero overtime and therefore may be provided so that it alternately perturbs theshuttles in one direction for half the time and in the other directionfor half the time. The test signal effectively modulates the motion ofthe shuttles in the Coriolis axis, so the induced accelerometer signalsare a product of the test signal with the motion of the shuttles.

When the modes are exactly matched, the test signal component of theCoriolis channel signals is output as just phase and the Coriolis signalis output as quadrature. When the modes are not exactly matched,however, some of the test signal shows up in the Coriolis channelsignals as quadrature (i.e., there will be an out-of-phase componentthat is used to produce the bias signal applied to the shuttles). Inorder to separate the signal components, the Coriolis signal isdemodulated against quadrature and the quadrature signal is demodulatedagainst phase, as described in greater detail below.

If necessary or desirable for a particular embodiment, the averagevoltage on the quadrature adjusting electrodes may be adjustedindependently of the test signal, for example, by a quadrature nullingservo with bandwidth much smaller than the test signal frequency. Thus,the effective quadrature output can be as near zero as is needed foraccuracy while leaving a modulated quadrature signal for use in the modefrequency matching servo. That modulated signal can be demodulatedagainst a product of the test signal with a shuttle frequency signal togive the desired servo error term. In embodiments that employ a digitaldemodulator (synchronous rectifier), this product can be formed, forexample, by forming an exclusive-or of the test and shuttle signals orby successive demodulation with those individual signals. There could bea residual ripple with zero mean at a harmonic of the test-signalfrequency even when the frequency servo is locked, although this shouldnot disturb the Coriolis signal if the test signal frequency is placedbeyond the pass band of the Coriolis output smoothing filter, asdiscussed more fully below.

FIG. 3 is a schematic block diagram showing electronic control circuitrysuitable for use with the gyroscope 100, in accordance with an exemplaryembodiment of the present invention. Among other things, the electroniccircuitry includes a biasing or mode matching servo 310, a quadratureservo 320, a phase servo 330, a shuttle resonance drive servo 340, aCoriolis output circuit 350, and related circuitry. These elements aredescribed below with reference to the idealized waveforms shown in FIGS.4-6.

The shuttle resonance drive servo 340 provides an alternating drivesignal to the drive combs based on signals received from the velocitysensing electrodes, as discussed above. If the drive is at the shuttleresonance frequency, then the velocity is in phase with it and,consequently, so is the Coriolis force. The shuttle resonance driveservo 340 also provides phase and quadrature reference signals from aphase-locked loop (PLL) circuit.

The quadrature servo 320 receives amplified (301) and filtered (302)Coriolis channel signals from the Coriolis-sensing (“Cor”) electrodes.As described below, the Coriolis channel signals include the Coriolissignals as well as signals induced by the electromechanical modulationof the shuttles in the Coriolis axis. The quadrature servo 320demodulates (321) the Coriolis channel signals with the quadraturereference and integrates (322) the demodulated signals to producelow-frequency differential quadrature nullifying signals that areamplitude modulated with the high-frequency test signal (which in thisexemplary embodiment is provided as a binary sub-multiple of the shuttleresonance mode frequency as shown by the addition of the fo/16 testfrequency by the two components 323 labeled “Σ”) and fed back to thequadrature adjustment (“Quad”) electrodes, as shown in FIG. 3 by thefeedback signals from the quadrature servo 320 to the Quad electrodes.Thus, a carrier modulated quadrature signal (mod_qd) appears along withthe Coriolis signal on the Cor electrodes. The quadrature servo 320 isconfigured to be too slow to respond to the test signal applied to thequadrature electrodes.

The phase servo 330 also receives the amplified (301) and filtered (302)Coriolis channel signals from the Cor electrodes. The phase servo 330demodulates (331) the Coriolis channel signals with the phase reference,which rectifies the Coriolis component to give an output with non-zerolow-frequency value (ph_demod_vel). The accompanying modulatedquadrature signal gives an output from that same demodulation processwhich cancels in a full cycle of the drive to yield no averagedisturbance (ph_demod_qd). If the accelerometer resonance mode is nottuned to exactly the shuttle resonance mode, then it responds to themodulated quadrature input with not only modulated quadrature but alsoan error component in phase with the Coriolis signal (ph_demod_err).This error signal also averages to zero each full cycle of the fo/16(carrier) test signal, producing no net output to interfere with thelow-pass filtered (332) version of the demodulated Coriolis signalpassed to the Coriolis output circuit 350 (i.e., the required gyroscopeoutput is effectively unperturbed by the test signal). In this exemplaryembodiment, the Coriolis signal is further filtered (333), remodulated(303) with the phase (drive) reference, and applied to thephase-compensating electrodes (112P, 114P, 116P, 118P, 120P, 122P, 124P,126P) to remove very low frequency gyroscope drift components, althoughthese components can be removed using other circuitry, so this feedbackloop and/or the specific phase electrodes shown in FIGS. 1 and 2 shouldbe considered optional with respect to embodiments of the presentinvention.

The mode matching servo 310 receives the output from the phase servodemodulator 331 and demodulates the signal with the fo/16 test signal,which converts both the Coriolis and modulated quadrature signals tozero-average components (car_demod_vel and car_demod_qd) and produces anerror component (car_demod_err) with a low-frequency value.Specifically, the mode matching servo demodulator 311 outputs a DCsignal proportional to the phase error, and the mode matching servointegrator 312 effectively removes the chopped up Coriolis signal andmagnifies the phase error. The sign and magnitude of that low frequencyphase error depend on the magnitude of the shuttle-to-accelerometermode-matching error and is used to servo the accelerometer resonancefrequency by (in this exemplary embodiment) placing a bias voltage onthe shuttles to nullify the result of further demodulation of thedemodulated phase signals from the phase servo 330 against the fo/16test signal (i.e., locking to 90 degrees phase shift), as shown in FIG.3 by the feedback signal to the Bias electrode. This bias adjustment isessentially a negative spring that effectively reduces the accelerometerresonance mode frequency. It should be noted that the present inventionis not limited to placing the bias voltage on the shuttles; rather, thebias voltage may be applied to other electrodes such as, for example,the quadrature adjusting electrodes or to separate mode adjustingelectrodes (not shown), although additional circuitry may be needed insuch alternative embodiments. As mentioned above, the test signalfrequency must be high enough for the quadrature servo 320 to notrespond and for the Coriolis output smoothing filter 332 of the phaseservo 330 to remove the test signal component, but also low enough forthe accelerometer physically to respond to the test signal so that thetest signal component shows up on the Cor electrodes. In practice, thequality factor (Q) of the accelerometer may slow its responsesufficiently to require some phase delay to the carrier demodulatorreference, which can be accomplished, for example, using a divider-basedPLL system.

The Coriolis output circuit 350 produces the gyroscope output signalbased on the demodulated and filtered Coriolis signal provided by thephase servo 330, a velocity (“Vel”) signal provided by the shuttleresonance drive servo 340, a scale factor (“SF”) obtained from anon-volatile memory, and a temperature signal (“T”) provided by atemperature sensor (not shown).

In the exemplary embodiment shown in FIG. 3, the amplifiers precedingthe quadrature demodulator 321 and phase demodulator 331 may betrans-resistance amplifiers. In an alternative embodiment, theamplifiers may be trans-capacitance amplifiers (which typically providelower-noise), in which case the quadrature and phase referencestypically would be swapped.

In the exemplary embodiment shown in FIGS. 1 and 2, each shuttleincludes plates that extend outwardly from the perimeter of the shuttle,with each plate completely overlaying a corresponding Coriolis(acceleration sensor) electrode and partially overlaying a pair ofquadrature electrodes on opposite sides of the Coriolis electrode, suchthat capacitive coupling between the plate and the quadrature electrodesis dependent on the rotational position of the shuttle while capacitivecoupling between the plate and the Coriolis electrode is substantiallyindependent of the rotational position of the shuttle. It should benoted, however, that different shuttle and/or electrode configurationsmay be used in alternative embodiments. For example, in certainalternative embodiments, portions of the shuttle perimeter may be incapacitive coupling with the Coriolis-sensing electrodes.

FIG. 7A and FIG. 7B is a schematic top-view diagram of a vibratorygyroscope in accordance with one alternative embodiment of the presentinvention. This vibratory gyroscope operates generally as the onedescribed above with reference to FIGS. 1 and 2, but is considered to bea simpler design by virtue of having fewer structures. Also, thepredominant gyroscope structures are oriented along the up and down axesor at 45 degree angles thereto, which facilitates micromachining becausemicromachining equipment (e.g., etching equipment) often produce etchesbased upon a rectilinear grid and so structures that are aligned withthe grid or at 45 degree angles thereto generally may be produced moreconsistently and with straighter edges.

It should be noted that the present invention is not limited to thegyroscope designs shown in FIGS. 1-2 and FIGS. 7A-7B. In variousalternative embodiments, gyroscopes having one, two, or more (e.g.,four) shuttles of the types shown and described in Geen, U.S. Pat. No.5,635,640 may be used. Furthermore, the present invention is not limitedto shuttles that oscillate rotationally but can be applied moregenerally to other types of inertial sensors, e.g., vibratory andtuning-fork type gyroscopes, that operate under similar principles, inwhich sensing mode motions can be induced by a separate test signal andnullified by an appropriately configured servo. In various embodiments,the sensing mode may be in-plane or out-of-plane compared with theresonator mode.

FIG. 8 is a schematic top-view diagram of a vibratory Z axis gyroscopein accordance with another alternative embodiment of the presentinvention. This gyroscope operates generally as disclosed in Geen, U.S.Pat. No. 6,877,374, which is hereby incorporated herein by reference inits entirety. Among other things, this gyroscope structure includes asubstantially square frame 210 that is suspended at its four corners byaccelerometer suspension flexures 202, 204, 206, and 208. On the outsidefour edges of the frame 210 are fingers 212, 213, 214, 215, 216, 217,218, and 219. Various resonating structures are suspended within theframe 210. These resonating structures include four movable shuttles220, 222, 224, and 226, four levers 228, 230, 232, and 234, and twoforks 236 and 238. It should be noted that the shuttles 222, 224, and226 are substantially the same shape, size, and mass as the shuttle 220,and are oriented as mirror images of the shuttle 220 along the x and/ory axes. It should be noted that the levers 230, 232, and 234 aresubstantially the same shape, size, and mass as the lever 228, and areoriented as mirror images of the lever 228 along the x and/or y axes.The four movable shuttles 220, 222, 224, and 226 are suspended from theframe 210 by flexures 240, 242, 244, and 246, respectively. Movement ofthe four movable shuttles 220, 222, 224, and 226 is controlledelectrostatically using electrostatic drivers 248, 250, 252, 254, 256,258, 260, and 262. There are also electrostatic structures associatedwith the levers 228, 230, 232, and 234 that can be used for drivingmotion of the levers or sensing motion of the levers. These and otherfeatures of the micromachined gyroscope structure are described in moredetail below.

The four accelerometer suspension flexures 202, 204, 206, and 208 areanchored to the substrate and are configured so as to substantiallyrestrict movement of the frame 210 along the x axis and along the y axis(i.e., translational movement) while allowing the frame 210 to rotatemore freely in either direction (i.e., rotational movement). Suchrotational movement of the frame 110 is caused mainly from the Corioliseffect due to movement of the frame of reference of the resonatingstructures.

The fingers 212, 213, 214, 215, 216, 217, 218, and 219 extend from thefour sides of the frame 210. Positioned between the fingers 212, 213,214, 215, 216, 217, 218, and 219 are two sets of Coriolis sensors thatare mechanically coupled to the substrate and do not move relative tothe substrate. Movement of the frame 210 results in movement of thefingers 212, 213, 214, 215, 216, 217, 218, and 219 relative to theCoriolis sensors, which produces a change in capacitance that can bemeasured by electronic circuitry (not shown).

The resonating structures, including the shuttles 220, 222, 224, and226, the flexures 240, 242, 244, and 246, the levers 228, 230, 232, and234, and the forks 236 and 238, are mechanically coupled. The shuttles220 and 222 are mechanically coupled via a pivot flexure 264, and theshuttles 224 and 226 are mechanically coupled via a pivot flexure 266.The shuttles 220 and 224 are mechanically coupled via the levers 228 and230 and the fork 236, and the shuttles 222 and 226 are mechanicallycoupled via the levers 232 and 234 and the fork 238. The pivot flexures264 and 266, the levers 228, 230, 232, and 234, and the forks 236 and238 allow the shuttles 220, 222, 224, and 226 to move together.

The shuttle 220 is suspended from the frame 210 by the flexure 240, fromthe shuttle 222 by the pivot flexure 264, and from the lever 228 by thepivot flexure 268. The shuttle 222 is suspended from the frame 210 bythe flexure 242, from the shuttle 220 by the pivot flexure 264, and fromthe lever 232 by the pivot flexure 272. The shuttle 224 is suspendedfrom the frame 210 by the flexure 244, from the shuttle 226 by the pivotflexure 266, and from the lever 230 by the pivot flexure 276. Theshuttle 226 is suspended from the frame 210 by the flexure 246, from theshuttle 224 by the pivot flexure 266, and from the lever 234 by thepivot flexure 280.

The lever 228 is suspended from the frame 210 by the pivot flexure 270,from the shuttle 220 by the pivot flexure 268, and from the lever 230 bythe fork 236. The lever 230 is suspended from the frame 210 by the pivotflexure 278, from the shuttle 224 by the pivot flexure 276, and from thelever 228 by the fork 236. The lever 232 is suspended from the frame 210by the pivot flexure 274, from the shuttle 222 by the pivot flexure 272,and from the lever 234 by the fork 238. The lever 234 is suspended fromthe frame 210 by the pivot flexure 282, from the shuttle 226 by thepivot flexure 280, and from the lever 232 by the fork 238.

The flexures 240, 242, 244, and 246 substantially restrict movement ofthe shuttles 220, 222, 224, and 226 respectively along the y axis, butallow movement of the shuttles 220, 222, 224, and 226 respectively alongthe x axis. The flexures 240, 242, 244, and 246 also allow the shuttles220, 222, 224, and 226 respectively to pivot slightly as they move.

The pivot flexure 264 essentially locks the shuttles 220 and 222together so that they move together. Likewise, the pivot flexure 266essentially locks the shuttles 224 and 226 together so that they movetogether (although oppositely to the shuttles 220 and 222).

The levers 228 and 230, the fork 236, and the pivot flexures 268, 270,276, and 278 essentially lock the shuttles 220 and 224 together so thatthey move in substantially equal but opposite directions. Likewise, thelevers 232 and 234, the fork 238, and the pivot flexures 272, 274, 280,and 282 essentially lock the shuttles 222 and 226 together so that theymove in substantially equal but opposite directions.

In theory, the various gyroscope structures are perfectly balanced sothat they move with substantially the same frequency and phase. Inpractice, however, the various gyroscope structures are not perfectlybalanced. For example, the shuttles 220, 222, 224, and 226 aretheoretically identical (albeit mirror images in the x and/or y axes),but typically are not identical due at least in part to variations inthe material and processes used to form the shuttles. Similar imbalancescan occur in other gyroscope structures, such as the various levers,pivots, and flexures. These imbalances can manifest themselves inout-of-phase (i.e., quadrature) lateral movements of the shuttles, whichcan vary from device to device. The mechanical stiffnesses of thestructures substantially suppresses these motions, but there is someresidual quadrature.

Therefore, electrical quadrature suppression structures are typicallyused to reduce the amount of quadrature, as discussed above. In anembodiment of the present invention, a quadrature suppression structuretypically includes at least one electrode located proximately to aportion of a shuttle along the direction of motion of the shuttle. Whena voltage is applied to the electrode, a resulting electrostatic forceproduces a lateral force that attracts the shuttle toward the electrode.A single electrode is typically associated with each shuttle, althoughnot all electrodes are typically activated. Rather, the quadraturebehavior of a particular device is typically characterized to determinewhich (if any) electrodes to activate to reduce the quadrature.

Because the amount of quadrature varies with the movement of theshuttle, it is desirable for the lateral force applied by the electrodeto likewise vary with the movement of the shuttle. In the embodimentshown in FIG. 8, variable-overlap quadrature adjusting electrodes areemployed. As shown in FIG. 9, two electrodes 1210 and 1220 are placedbetween two adjacent shuttles 220 and 222, specifically in a cavity 1200formed in and by the two shuttles 220 and 222 (similar electrodes areplaced between the shuttles 224 and 226). The electrode 1210 is adjacentto the shuttle 220, and is capable of applying a lateral force on theshuttle 220 in the downward direction. The electrode 1220 is adjacent tothe shuttle 222, and is capable of applying a lateral force on theshuttle 222 in the upward direction. In order to vary the amount oflateral force applied by an electrode, a notch is formed in eachshuttle. The notch is formed adjacent to a portion of the electrodetoward the end of the electrode closer to the frame. As the shuttlemoves outward toward the frame, the length of shuttle that is directlyadjacent to the electrode increases, resulting in a larger lateral forceapplied to the shuttle. As the shuttle moves inward away from the frame,the length of shuttle that is directly adjacent to the electrodedecreases, resulting in a smaller lateral force applied to the shuttle.In order to cancel out static forces, it is common to activate oneelectrode between the shuttles 220 and 222 and one electrode between theshuttles 224 and 226. Also, a constant voltage is typically applied forthe sake of simplicity, although a variable voltage could be used at thecost of increased complexity.

As in the exemplary embodiments described above with reference to FIGS.1-2 and FIGS. 7A-7B, in order to match the shuttle resonance mode andthe accelerometer resonance mode, a high-frequency test (carrier) signalmay be used to modulate the motion of the shuttles to produce a nettorque on the frame so as to induce accelerometer signals in theCoriolis channel that are 90 degrees phase shifted with respect to theCoriolis acceleration signal, and the accelerometer resonance mode maybe adjusted by providing an appropriate biasing signal. In certainembodiments, the high-frequency test signal may be applied to thevariable-overlap quadrature adjusting electrodes to induce theaccelerometer signals in the Coriolis channel (i.e., the quadratureadjusting electrodes generate a quadrature output modulated by the inputtest signal). The test signal is provided in an asymmetric fashion suchthat the modulated motion of the shuttles produces a net force on theframe to induce the accelerometer signals, unlike the driver andquadrature adjusting signals, which are intended to prevent the motionof the shuttles from producing a net force on the frames. The biassignal may be applied between the Coriolis pickoff electrodes and theframes or to other appropriate structures. Thus, the test signal appliedto the quadrature adjusting electrodes causes the quadrature motion ofthe shuttles to be amplitude modulated with the test frequency in thedevice plane. The test signal is provided at a frequency sufficientlyabove the gyroscope response frequency, so that the induced signal isnot detected by the signal filtering in the Coriolis channel andtherefore does not affect the gyroscope output, but at a frequencysufficiently below the accelerometer resonance mode frequency, so thatthe Coriolis accelerometer will respond to the test signals.Furthermore, the test signal preferably averages to zero over time andtherefore may be provided so that it alternately perturbs the shuttlesin one direction for half the time and in the other direction for halfthe time. The test signal effectively modulates the motion of theshuttles in device plane, so the induced accelerometer signals are aproduct of the test signal with the motion of the shuttles.

FIG. 10 is a schematic top-view diagram of a cross-quad Z axis gyroscopein accordance with another alternative embodiment of the presentinvention. This gyroscope operates generally as disclosed in Geen, U.S.Pat. No. 7,421,897, which is hereby incorporated herein by reference inits entirety. Specifically, four gyroscopes 16A-D are arranged in avertically and horizontally coupled cross-quad configuration such thatthe top pair of gyroscope frames and the bottom pair of gyroscope framesare interconnected by couplings 99 that allow anti-phase movements ofthe frames along separate parallel Y axes, while the left side pair ofgyroscope frames and the right side pair of gyroscope frames areinterconnected by couplings 95 that allow co-linear anti-phase movementsof the frames. Each gyroscope is preferably supported on the sideopposite the vertical coupling 95 by a suspension 93. Each gyroscope ispreferably supported on the side opposite the horizontal coupling 99 bya balancer 97 that offsets certain effects of the horizontal coupling.The gyroscopes 16A-D may be similar to the gyroscopes disclosed in U.S.Pat. Nos. 6,505,511 and 6,122,961, which are hereby incorporated hereinby reference in their entireties.

FIG. 11 shows a specific cross-quad gyroscope configuration that can beadapted for mode matching, in accordance with another alternativeembodiment of the present invention. Here, each gyroscope 50A, 50B, 50C,50D includes a frame (52A, 52B, 52C, 52D) and a resonator (54A, 54B,54C, 54D) movably suspended within the inner periphery of the frame. Theframes 52A and 52B of gyroscopes 50A and 50B are coupled to one another,as are the frames 52C and 52C of gyroscopes 50C and 50D. Furthermore,the frames 52A and 52C of gyroscopes 50A and 50C are coupled to oneanother, as are the frames 52B and 52D of gyroscopes 50B and 50D.

The resonators of each pair of gyroscopes 50A/50B and 50C/50D operate inanti-phase to one another. Furthermore, in an exemplary embodiment ofthe invention, the resonators of gyroscopes 50A and 50B operate inanti-phase to the corresponding resonators of gyroscopes 50C and 50D.Therefore, the resonators of gyroscopes that are diagonally oppositeoperate in phase with one another, while the resonators of any pair ofadjacent gyroscopes operate in anti-phase with one another.

Also, the frames of each pair of gyroscopes 50A/50B and 50C/50D arecoupled to allow movement in opposite directions but substantiallyrestrict movement in the same direction. Furthermore, in accordance withan exemplary embodiment of the invention, the frames of gyroscopes 50Aand 50C are coupled to allow movement in opposite directions butsubstantially restrict movement in the same direction, as are frames ofgyroscopes 50B and 50D. The frames of gyroscopes 50A/50C move inanti-phase to the frames of gyroscopes 50B/50D. Therefore, the frames ofgyroscopes that are diagonally opposite operate in phase with oneanother, while the frames of any pair of adjacent gyroscopes operate inanti-phase with one another.

The resonators are caused to resonate back and forth in the X-axis.Rotation of the inertial sensor about the Z-axis causes displacement ofthe frames in the Y-axis. For example, under some conditions, frames 52Aand 52C of gyroscopes 50A and 50C move toward one another while frames52B and 52D of gyroscopes 50B and 50D move away from one another. Undersome other conditions, frames 52A and 52C of gyroscopes 50A and 50C moveaway from one another while frames 52B and 52D of gyroscopes 50B and 50Dmove toward one another.

As in the exemplary embodiments described above, in order to match theshuttle resonance mode and the accelerometer resonance mode, ahigh-frequency test (carrier) signal may be used to modulate the motionof the shuttles to produce Y-axis forces on the frame so as to induceaccelerometer signals in the Coriolis channel that are 90 degrees phaseshifted with respect to the Coriolis acceleration signal, and theaccelerometer resonance mode may be adjusted by providing an appropriatebiasing signal. In certain embodiments, the high-frequency test signalmay be applied to variable-overlap electrodes to induce theaccelerometer signals in the aggregated Coriolis channel (i.e., theelectrodes generate a quadrature output modulated by the input testsignal). FIG. 12 shows an electrode configuration for an exemplaryembodiment, including two electrodes 55 positioned within notchedcavities in the surrounding shuttle 54 to produce Y-axis forces as theshuttle resonates in the X-axis so as to vary the amount of overlapbetween each electrode 55 and the portions of the shuttle 54 adjacentthereto; in various alternative embodiments, one or more such electrodeconfigurations may be used for each shuttle (e.g., one set or twomirror-image sets positioned substantially in the middle of each shuttleor four mirror-image sets positioned toward the corners of eachshuttle), with the electrodes of each set driven by the outputs of adifferential amplifier and the electrodes for shuttles 54A/D operatingin phase with one another and the electrodes for shuttles 54B/Coperating in phase with one another and in anti-phase with theelectrodes of shuttles 54A/D. The test signal is provided in anasymmetric fashion such that the modulated motion of the shuttlesproduces a net force on the frames to induce the accelerometer signals,unlike the driver and quadrature adjusting signals, which are intendedto prevent the motion of the shuttles from producing a net force on theframes. The bias signal may be applied between the Coriolis pickoffelectrodes and the frames or to other appropriate structures. Thus, thetest signal applied to the quadrature adjusting electrodes causes thequadrature motion of the shuttles to be amplitude modulated with thetest frequency in the device plane. The test signal is provided at afrequency sufficiently above the gyroscope response frequency, so thatthe induced signal is not detected by the signal filtering in theCoriolis channel and therefore does not affect the gyroscope output, butat a frequency sufficiently below the accelerometer resonance modefrequency, so that the Coriolis accelerometer will respond to the testsignals. Furthermore, the test signal preferably averages to zero overtime and therefore may be provided so that it alternately perturbs theshuttles in one direction for half the time and in the other directionfor half the time. The test signal effectively modulates the motion ofthe shuttles in device plane, so the induced accelerometer signals are aproduct of the test signal with the motion of the shuttles.

It should be noted that the bias signal may affect the magnitude ofquadrature correction and other device parameters (e.g., the Coriolisscale factor). In exemplary embodiments, the quadrature servoautomatically compensates for the bias signal, and the Coriolis scalefactor similarly is compensated in the electronics.

The embodiments of the invention described above are intended to bemerely exemplary; numerous variations and modifications will be apparentto those skilled in the art. All such variations and modifications areintended to be within the scope of the present invention as defined inany appended claims.

What is claimed is:
 1. An inertial sensor comprising: a substrate havinga plurality of electrode arrangements, each electrode arrangementincluding an acceleration sensor electrode and a pair of quadratureadjusting electrodes on opposite sides of the acceleration sensorelectrode; and a resonator disposed in a device layer above thesubstrate and having at least one shuttle including a plurality ofplates, each plate completely overlaying a corresponding accelerationsensor electrode and partially overlaying the pair of quadratureadjusting electrodes on opposite sides of the acceleration sensorelectrode, such that capacitive coupling between the plate and each ofthe quadrature adjusting electrodes is dependent upon the rotationalposition of the at least one shuttle while capacitive coupling betweenthe plate and the acceleration sensor electrodes is substantiallyindependent of the rotational position of the at least one shuttle. 2.An inertial sensor according to claim 1, further comprising: a pluralityof drive electrodes disposed in the device layer for rotationallydithering the at least one shuttle in a device layer plane.
 3. Aninertial sensor according to claim 2, further comprising: a shuttleresonance drive servo coupled to the drive electrodes, the shuttleresonance drive servo configured to provide drive signals to the driveelectrodes for rotationally dithering the at least one shuttle in thedevice layer plane.
 4. An inertial sensor according to claim 1, furthercomprising: a quadrature servo coupled to the quadrature adjustingelectrodes, the quadrature servo configured to provide quadraturenullifying signals to the quadrature adjusting electrodes.
 5. Aninertial sensor according to claim 4, wherein the quadrature nullifyingsignals are DC quadrature adjustment signals.
 6. An inertial sensoraccording to claim 1, wherein each shuttle includes an outer rimsuspended via a number of spokes from a central hub.
 7. An inertialsensor according to claim 6, wherein the substrate further comprises,for each of a number of spokes, a pair of quadrature adjustingelectrodes on the substrate underlying the radial edges of the spoke. 8.An inertial sensor according to claim 7, further comprising: aquadrature servo coupled to the quadrature adjusting electrodes of theelectrode arrangements and coupled to the quadrature adjustingelectrodes underlying the radial edges of the spokes, the quadratureservo configured to provide quadrature nullifying signals to thequadrature adjusting electrodes.
 9. An inertial sensor according toclaim 8, wherein the quadrature nullifying signals are DC quadratureadjustment signals.
 10. An inertial sensor according to claim 1, furthercomprising: a test signal generator coupled to the quadrature adjustingelectrodes, the test signal generator configured to provide a testsignal to the quadrature adjusting electrodes at a test signal frequencyabove a predetermined quadrature servo response frequency.
 11. Aninertial sensor according to claim 10, further comprising: a modematching servo coupled to the test signal generator and to theacceleration sensor electrodes, the mode matching servo configured todemodulate acceleration sensor signals received from the accelerationsensor electrodes with the test signal received from the test signalgenerator and to produce therefrom a bias signal.
 12. An inertial sensoraccording to claim 11, wherein the mode matching servo is coupled to theat least one shuttle to place the bias signal on the at least oneshuttle.
 13. An inertial sensor according to claim 11, wherein the modematching servo is coupled to an electrode on the substrate underlyingthe at least one shuttle to place the bias signal on the said electrode.14. An inertial sensor according to claim 1, wherein each electrodearrangement further includes a phase-compensating electrode.
 15. Aninertial sensor according to claim 1, wherein the resonator includes twoshuttles that are mechanically coupled by a coupling flexure to ensurethat the shuttles oscillate in anti-phase with one another.
 16. Anapparatus for use with a resonator having at least one shuttle includinga plurality of plates, the apparatus comprising: a substrate having aplurality of electrode arrangements, each electrode arrangementincluding an acceleration sensor electrode and a pair of quadratureadjusting electrodes on opposite sides of the acceleration sensorelectrode, each electrode arrangement capable of being overlaid by acorresponding plate of the at least one shuttle such that the platecompletely overlays the acceleration sensor electrode and partiallyoverlays the pair of quadrature adjusting electrodes on opposite sidesof the acceleration sensor electrode such that capacitive couplingbetween the plate and each of the quadrature adjusting electrodes isdependent upon the rotational position of the at least one shuttle whilecapacitive coupling between the plate and the acceleration sensorelectrodes is substantially independent of the rotational position ofthe at least one shuttle.
 17. An apparatus according to claim 16,wherein the substrate further comprises at least one electricalconnection for providing quadrature nullifying signals to the quadratureadjusting electrodes.
 18. An apparatus according to claim 16, whereinthe substrate further comprises: at least one pair of quadratureadjusting electrodes on the substrate configured to be overlaid by theradial edges of a corresponding spoke of the at least one shuttle. 19.An apparatus according to claim 18, wherein the substrate furthercomprises at least one electrical connection for providing quadraturenullifying signals to the quadrature adjusting electrodes of theelectrode arrangements and to the quadrature adjusting electrodesunderlying the radial edges of the spokes.
 20. An apparatus according toclaim 16, wherein each electrode arrangement further includes aphase-compensating electrode.